Hardback
Series: Cambridge Series in Statistical and Probabilistic Mathematics (No. 33)
ISBN: 9781107008007
2 b/w illus. 350 exercises
Dimensions: 253 x 215 mm
available from August 2011
This comprehensive guide to stochastic processes gives a complete overview of the theory and addresses the most important applications. Pitched at a level accessible to beginning graduate students and researchers from applied disciplines, it is both a course book and a rich resource for individual readers. Subjects covered include Brownian motion, stochastic calculus, stochastic differential equations, Markov processes, weak convergence of processes and semigroup theory. Applications include the Black?Scholes formula for the pricing of derivatives in financial mathematics, the Kalman?Bucy filter used in the US space program and also theoretical applications to partial differential equations and analysis. Short, readable chapters aim for clarity rather than full generality. More than 350 exercises are included to help readers put their new-found knowledge to the test and to prepare them for tackling the research literature.
Paperback
ISBN: 9781107647831
750 b/w illus. 200 exercises
Dimensions: 246 x 189 mm
available from October 2011
This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of special symbols. The authors have also revised many of the end-of-chapter exercises to make them more challenging and to include some interesting new results. Full solutions to the 200 problems are included in the text, while complete solutions to all of the end-of-chapter exercises are available in a new Instructors' Manual, which can be downloaded from www.cambridge.org/9781107647831.
Preface
Introduction: geometry and geometries
1. Conics
2. Affine geometry
3. Projective geometry: lines
4. Projective geometry: conics
5. Inversive geometry
6. Hyperbolic geometry: the disc model
7. Elliptic geometry: the spherical model
8. The Kleinian view of geometry
Special symbols
Further reading
Appendix 1. A primer of group theory
Appendix 2. A primer of vectors and vector spaces
Appendix 3. Solutions to the problems
Index.
Hardback
ISBN: 9781107010871
Paperback
ISBN: 9780521283045
10 tables 220 exercises
Dimensions: 228 x 152 mm
available from October 2011
Preface
1. Categories
2. Basic gadgetry
3. Functors and natural transformations
4. Limits and colimits in general
5. Adjunctions
6. Posets and monoid sets
Bibliography
Index.
2011 | Hardcover
ISBN 978-3-11-020717-0
Series: De Gruyter Expositions in Mathematics 56
to be published June 2011
24 x 17 cm
xxvi, 639 pages
Languages: English
Type of Publication: Monograph
This is the last of three volumes of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume:
impact of minimal nonabelian subgroups on the structure of p-groups,
classification of groups all of whose nonnormal subgroups have the same order,
degrees of irreducible characters of p-groups associated with finite algebras,
groups covered by few proper subgroups,
p-groups of element breadth 2 and subgroup breadth 1,
exact number of subgroups of given order in a metacyclic p-group,
soft subgroups,
p-groups with a maximal elementary abelian subgroup of order p2,
p-groups generated by certain minimal nonabelian subgroups,
p-groups in which certain nonabelian subgroups are 2-generator.
The book contains many dozens of original exercises (with difficult exercises being solved) and a list of more than 1000 research
problems and themes.
Mathematics > Mathematics, General
Mathematics > Algebra, Number theory
Group Theory; Order; Prime
2011 | Hardcover
ISBN 978-3-11-025408-2
Series: De Gruyter Studies in Mathematics 41
to be published August 2011
24 x 17 cm
Approx. x, 310 pages
Languages: English
Type of Publication: Monograph
With exercises and many open questions for further investigations on different levels of difficulty
Presents good starting points for a Bachelor, Master or even PhD thesis
This is a highly self-contained book about algebraic graph theory which is written with a view to keep the lively and unconventional
atmosphere of a spoken text to communicate the enthusiasm the author feels about this subject. The focus is on homomorphisms
and endomorphisms, matrices and eigenvalues.
Graph models are extremely useful for almost all applications and applicators as they play an important role as structuring tools.
They allow to model net structures - like roads, computers, telephones - instances of abstract data structures - like lists, stacks,
trees - and functional or object oriented programming.
Mathematics > Algebra, Number theory
Mathematics > Combinatorics and Graph Theory
Graph Theory; Algebra; Matrices; Monoids; Morphisms